Landing Probabilities of Random Walks for Seed-Set Expansion in Hypergraphs Eli Chien Pan Li Olgica Milenkovic Department ECE, UIUC Department ECE, UIUC Department ECE, UIUC Abstract We describe the first known mean-field study of landing probabilities for random walks on hypergraphs. In particular, we examine clique-expansion and tensor methods and evaluate their mean-field characteristics over a class of random hypergraph models for the purpose of seed-set community expansion. We describe parameter regimes in which the two methods outperform each other and propose a hybrid expansion method that uses partial clique-expansion to reduce the projection distortion and low-complexity tensor methods applied directly on the partially expanded hypergraphs. 1 1 Introduction Random walks on graphs are Markov random processes in which given a starting vertex, one moves to a randomly selected neighbor and then repeats the procedure starting from the newly selected vertex [1]. Random walks are used in many graph-based learning algorithms such as PageRank [2] and Label Propagating [3], and they have found a variety of applications in local community detection [4, 5], information retrieval [2] and semi-supervised learning [3]. Random walks are also frequently used to characterize the topological structure of graphs via the hitting time of a vertex from a seed, the commute time between two vertices [6] and the mixing time which also characterizes global graph connectivity [7]. Recently, a new measure of vertex connectivity and similarity, termed a landing probability (LP), was introduced in [8]. A1 Eli Chien and Pan Li contribute equally to this work.Preprint version. LP of a vertex is the probability of a random walk ending at the vertex after making a certain number of steps. Different linear combinations of LPs give rise to different forms of PageRanks (PRs), such as the standard PR [2] and the heat-kernel PR [9], both used for various graph clustering tasks. In particular, Kloumann et al. [8] also initiated the analysis of PRs based on LPs for seed-based community detection. Under the assumption of a generative stochastic block model (SBM) [10] with two blocks, the authors of [8] proved that the empirical average of LPs within the seed community concentrates around a deterministic centroid. Similarly, the empirical averages of LPs outside the seed community also concentrate around another deterministic centroid.

Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data such as images. Learning a lower-dimensional embedding that can better reflect the geometry of the dataset is therefore instrumental for performance. We propose a new approach for this task where the embedding is performed by a differentiable model such as a deep neural network. By rewriting the $k$-means clustering algorithm as an optimal transport task, and adding an entropic regularization, we derive a fully differentiable loss function that can be minimized with respect to both the embedding parameters and the cluster parameters via stochastic gradient descent. We show that this new formulation generalizes a recently proposed state-of-the-art method based on soft-$k$-means by adding constraints on the cluster sizes. Empirical evaluations on image classification benchmarks suggest that compared to state-of-the-art methods, our optimal transport-based approach provide better unsupervised accuracy and does not require a pre-training phase.

Motivated by the idea of turbomachinery active subspace performance maps, this paper studies dimension reduction in turbomachinery 3D CFD simulations. First, we show that these subspaces exist across different blades---under the same parametrization---largely independent of their Mach number or Reynolds number. This is demonstrated via a numerical study on three different blades. Then, in an attempt to reduce the computational cost of identifying a suitable dimension reducing subspace, we examine statistical sufficient dimension reduction methods, including sliced inverse regression, sliced average variance estimation, principal Hessian directions and contour regression. Unsatisfied by these results, we evaluate a new idea based on polynomial variable projection---a non-linear least squares problem. Our results using polynomial variable projection clearly demonstrate that one can accurately identify dimension reducing subspaces for turbomachinery functionals at a fraction of the cost associated with prior methods. We apply these subspaces to the problem of comparing design configurations across different flight points on a working line of a fan blade. We demonstrate how designs that offer a healthy compromise between performance at cruise and sea-level conditions can be easily found by visually inspecting their subspaces.

This paper proposes a new evaluation metric and boosting method for weight separability in neural network design. In contrast to general visual recognition methods designed to encourage both intra-class compactness and inter-class separability of latent features, we focus on estimating linear independence of column vectors in weight matrix and improving the separability of weight vectors. To this end, we propose an evaluation metric for weight separability based on semi-orthogonality of a matrix and Frobenius distance, and the feed-backward reconstruction loss which explicitly encourages weight separability between the column vectors in the weight matrix. The experimental results on image classification and face recognition demonstrate that the weight separability boosting via minimization of feed-backward reconstruction loss can improve the visual recognition performance, hence universally boosting the performance on various visual recognition tasks.

Designing artificial intelligence for games (Game AI) has been long recognized as a notoriously challenging task in game industry, as it mainly relies on manual design, requiring plenty of domain knowledge. More frustratingly, even spending a lot of efforts, a satisfying Game AI is still hard to achieve by manual design due to the almost infinite search space. The recent success of deep reinforcement learning (DRL) sheds light on advancing automated game designing, significantly relaxing human competitive intelligent supp ort. However, existing DRL algorithms mostly focus on training a Game AI to win the game rather that the way it wins (style). To bridge the gap, we introduce EMO-DRL, an end-to-end game design framework, leveraging evolutionary algorithm, DRL and multi-objective optimization (MOO) to perform intelligent and automatic game design. Firstly, EMO-DRL proposes the style-oriented learning to bypass manual reward shaping in DRL and directly learns a Game AI with an expected style in an end-to-end fashion. On this basis, the prioritized multi-objective optimization is introduced to achieve more diverse, nature and humanlike Game AI. Large-scale evaluations on a Atari game and a commercial massively mul-tiplayer online game are conducted. The results demonstrat es that EMO-DRL, compared to existing algorithms, achieve better game designs in an intelligent and automatic way.

We consider the task of learning a causal graph in the presence of latent confounders given i.i.d.~samples from the model. While current algorithms for causal structure discovery in the presence of latent confounders are constraint-based, we here propose a score-based approach. We prove that under assumptions weaker than faithfulness, any sparsest independence map (IMAP) of the distribution belongs to the Markov equivalence class of the true model. This motivates the \emph{Sparsest Poset} formulation - that posets can be mapped to minimal IMAPs of the true model such that the sparsest of these IMAPs is Markov equivalent to the true model. Motivated by this result, we propose a greedy algorithm over the space of posets for causal structure discovery in the presence of latent confounders and compare its performance to the current state-of-the-art algorithms FCI and FCI+ on synthetic data.

Incorporating human expertise and domain knowledge is particularly important for medical image processing applications, marked with small datasets, and objects of interests in the form of organs or lesions not typically seen in traditional datasets. However, the incorporation of prior knowledge for breast tumor detection is challenging, since shape, boundary, curvature, intensity, or other common medical priors vary significantly across patients and cannot be employed. This work proposes an approach for integrating visual saliency into a deep learning model for breast tumor segmentation in ultrasound images. Visual saliency emphasizes regions that are more likely to attract radiologists' visual attention and stand out from its surrounding. Our approach is based on a U-Net model and employs attention blocks to introduce visual saliency. Such model forces learning feature representations that prioritize spatial regions with high levels of saliency. The approach is validated using a dataset of 510 breast ultrasound images.

From two unlabeled (U) datasets with different class priors, we can train a binary classifier by empirical risk minimization, which is called UU classification. It is promising since UU methods are compatible with any neural network (NN) architecture and optimizer as if it is standard supervised classification. In this paper, however, we find that UU methods may suffer severe overfitting, and there is a high co-occurrence between the overfitting and the negative empirical risk regardless of datasets, NN architectures, and optimizers. Hence, to mitigate the overfitting problem of UU methods, we propose to keep two parts of the empirical risk (i.e., false positive and false negative) non-negative by wrapping them in a family of correction functions. We theoretically show that the corrected risk estimator is still asymptotically unbiased and consistent; furthermore we establish an estimation error bound for the corrected risk minimizer. Experiments with feedforward/residual NNs on standard benchmarks demonstrate that our proposed correction can successfully mitigate the overfitting of UU methods and significantly improve the classification accuracy.

In this paper we examine a formalization of feature distribution learning (FDL) in information-theoretic terms relying on the analytical approach and on the tools already used in the study of the information bottleneck (IB). It has been conjectured that the behavior of FDL algorithms could be expressed as an optimization problem over two information-theoretic quantities: the mutual information of the data with the learned representations and the entropy of the learned distribution. In particular, such a formulation was offered in order to explain the success of the most prominent FDL algorithm, sparse filtering (SF). This conjecture was, however, left unproven. In this work, we aim at providing preliminary empirical support to this conjecture by performing experiments reminiscent of the work done on deep neural networks in the context of the IB research. Specifically, we borrow the idea of using information planes to analyze the behavior of the SF algorithm and gain insights on its dynamics. A confirmation of the conjecture about the dynamics of FDL may provide solid ground to develop information-theoretic tools to assess the quality of the learning process in FDL, and it may be extended to other unsupervised learning algorithms.

Neural sequence-to-sequence models provide a competitive approach to the task of mapping a question in natural language to an SQL query, also referred to as text-to-SQL generation. The Byte-Pair Encoding algorithm (BPE) has previously been used to improve machine translation (MT) between natural languages. In this work, we adapt BPE for text-to-SQL generation. As the datasets for this task are rather small compared to MT, we present a novel stopping criterion that prevents overfitting the BPE encoding to the training set. Additionally, we present AST BPE, which is a version of BPE that uses the Abstract Syntax Tree (AST) of the SQL statement to guide BPE merges and therefore produce BPE encodings that generalize better. W e improved the accuracy of a strong attentive seq2seq baseline on five out of six English text-to-SQL tasks while reducing training time by more than 50% on four of them due to the shortened targets. Finally, on two of these tasks we exceeded previously reported accuracies.